This paper presents an analytical method to design a mechanical finger for robotic manipulations. As traditional mechanical fingers require bulky electro-magnetic motors and numerous relative-moving parts to achieve dexterous motion, we propose a class of fingers the manipulation of which relies on finger deflections. These compliant fingers are actuated by shape memory alloy (SMA) wires that exhibit high workdensity, frictionless, and quite operations. The combination of compliant members with embedded SMA wires makes the finger more compact and lightweight. Various SMA wire layouts are investigated to improve their response time while maintaining sufficient output force. The mathematical models of finger deflection caused by SMA contraction are then derived along with experimental validations. As finger shapes are essential to the range of deflected motion and output force, we find its optimal initial shapes through the use of a shape parameterization technique. We further illustrate our method by designing a humanoid finger that is capable of threedimensional manipulation. As compliant fingers can be fabricated monolithically, we expect the proposed method to be utilized for applications of various scales.